JP2010223670A - Optical tomographic image display system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To display a tomogram with high precision in an optical tomogram display system. <P>SOLUTION: In the optical tomogram display system of a frequency region, the frequency analysis of interference light is performed to obtain an optical tomogram. At this time, frequency f', amplitude A' and an initial phase ϕ' are calculated so that the sum square of the difference between an interference signal being an analyzing target signal and a sine wave model signal shown by a phase using the frequency f' and the initial phase ϕ' and the amplitude A' may become the minimum value, and the tomogram is displayed by the analyzing result thereof. By this method, the optical tomogram of high precision is obtained. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an optical tomographic image display system characterized by signal processing.

  In recent years, with the advancement of medical techniques such as endoscopic treatment, a diagnostic method that performs non-intrusive and real-time diagnosis of pathological tissue is desired. Conventionally, for example, an electronic endoscope using a CCD, imaging using CT, MRI, and ultrasonic waves are used as diagnostic methods. The electronic endoscope is limited to observation of the surface of a living body, and the latter diagnostic imaging system has a technical limit in observing with a resolution of micron order. An optical coherence tomography system (OCT) has attracted attention as a technique that complements such a method.

  There are two types of OCT: time-domain OCT (TD-OCT) and frequency-domain OCT (FD-OCT). Also in FD-OCT, spectrometer type (SD-OCT) and wavelength scanning light source There are two types (SS-OCT). In the case of the conventional time domain OCT, the interference component of the reflected light from the inside of the living body was subjected to frequency analysis by applying broadband light, but this method also overlaps the reflected light from different depths in the interference light. Therefore, only signal light from a specific depth could not be detected with high sensitivity.

  On the other hand, as shown in Patent Document 1, a spectrometer-type OCT irradiates a living body with light from a white light source, and interferes with reference light and reflected light returning from different depths in the living body with an interferometer. Let Then, the reflected light is dispersed by a diffraction grating or the like and received by a one-dimensional CCD to obtain an electric signal. As described in Patent Document 2, the wavelength scanning type OCT irradiates a living body with light, continuously changes the wavelength of the irradiation light, and returns from the reference light and a different depth in the living body. With an interferometer. These are all systems that obtain tomographic images by analyzing the frequency components of interference signals. In FD-OCT, the obtained interference signal light is Fourier transformed to obtain a tomographic image. Since this technique can construct a high-resolution tomographic image, it is expected as an advanced system, and theoretically, a sensitivity of 100 times or more of time domain OCT can be obtained. The wavelength scanning type OCT is suitable for practical use such as an endoscope in that it has high measurement sensitivity and is resistant to dynamic noise. Here, the wider the wavelength scanning band of the irradiated light, the higher the frequency analysis band, so that the resolution in the depth direction increases.

  However, FD-OCT has a drawback in that the resolution is limited because side lobes other than the main lobe are generated due to the influence of the window during Fourier transform. This problem will be described below.

  Conventionally, as a signal analysis method using a sine wave model using Fourier transform, various methods have been proposed, as introduced in Non-Patent Document 1, but most of them have previously set the signal frequency in advance. And obtaining the optimum amplitude and initial phase at the estimated frequency.

  The signal is a superposition of sine waves having a plurality of frequencies, and in order to analyze the signal, frequency parameters such as amplitude and initial phase are estimated for each sine wave having various frequencies constituting the signal. As such a frequency analysis method, Fourier transform is widely known. In the case of a periodic signal, the estimation of the frequency parameter in the Fourier transform can be performed by using a Fourier transform equation with a finite-length window as shown in the following equation (1). Based on, parameters (amplitude A and initial phase φ) of a specific frequency f (= n / T: n is an integer, T is an analysis window length) can be estimated. However, the relationship between the amplitude A, the initial phase φ, and X (f) is expressed by the following equation (2).

  The frequency parameter that can be estimated by such Fourier transform depends on the analysis window length T, and can only be calculated for a frequency that is an integral multiple of 1 / T. Therefore, as long as the parameter is estimated using the above equation (1), the frequency f is theoretically discrete and the frequency component of the aperiodic signal cannot be specified. In addition, in most fields where frequency analysis is performed using Fourier transform, it is extremely difficult to perform integration calculations over an infinitely long integration interval, even though non-periodic signals with no period are to be analyzed. For this reason, the above equation (1) must be used.

  In order to solve this problem, there is an attempt to improve the apparent frequency resolution by using a plurality of window function adjustments and analysis intervals.

  For example, the short-time Fourier transform (Short-Time Fourier Transform; STFT) described in Non-Patent Document 2 divides an acoustic signal into a plurality of signals by a short-time analysis window. In this method, Fourier transform is performed independently.

  In the ABS (Analysis by Synthesis) method and GHA (Generalized Harmonic Analysis) described in Non-Patent Document 3 to Non-Patent Document 6, a plurality of frequencies for determining the optimum frequency are prepared and the amplitude and initial phase are set. The optimum combination of frequency, amplitude, and initial phase is selected from these.

JP 2006-132996 A JP 2007-024677 A

Mikio Higashiyama, Tsunehiko Koike, "Signal analysis method with high frequency analysis accuracy", Transactions of the Acoustical Society of Japan, 1988, Vol. 54, No. 8 L. R. Rabiner and R. W. Schafer, "Digital Processing of Speech Signals", Prentice-Hall, Englewood Cliffs, NJ, 1978 T. F. Quatieri and R. J. McAulay, "Speech transformations based on a sinesoidal representation", IEEE Trans. Acoust. Speech Signal Process. ASSP 34, 1986, p. 1449-1464 E. B. George and M. J. Smith, "Analysis-by-synthesis / overlap-add sinusoidal representation", J. Audio Eng. Soc. 40, 1992, p.497-515 E. B. George and M. J. Smith, "Speech analysis / synthesis and modification using an analysis-by-synthesis / overlap-add sinusoidal model", IEEE Trans. Speech Audio Process. 5, 1997, p.389-406 T. Terada, H. Nakajima, M. Tohyama and Y. Hirata, "Non-stationary waveform analysis and synthesis using generalized harmonic analysis", IEEE-SP, Int. Symp. TF / TS Analysis, 1994, p.429- 432

  However, the short-time Fourier transform described in Non-Patent Document 2 still has a problem that the frequency parameter can be estimated only at a frequency that is an integer multiple of the reciprocal of the short-time analysis window length.

  In the ABS method, GHA, and the like described in Non-Patent Document 3 to Non-Patent Document 6 described above, if there is a frequency different from the frequency prepared in advance for the original signal, an incorrect combination is found. There is a problem that a plurality of detections are performed and the analysis accuracy is lowered.

The attempt to improve the apparent frequency resolution by using these window function adjustments and multiple analysis intervals is as follows:
1) To increase the frequency resolution, the analysis window length must be increased. However, for signals with temporal frequency fluctuations, the frequency is averaged, making it difficult to capture temporal fluctuations. It has been pointed out that the frequency resolution decreases when the analysis window length is shortened.

  As described above, capturing the change in frequency finely and increasing the frequency resolution have a mutually contradictory relationship, which has been a major problem in signal analysis.

  The present invention has been made in view of such a situation, and in an optical tomographic image display system, the frequency resolution has high frequency resolution without depending on the analysis window length, and frequency analysis can be performed with high accuracy. It is an object of the present invention to provide an optical tomographic image display system capable of displaying an image with high resolution, high sensitivity, and high speed.

  In order to solve this problem, an optical tomographic image display system according to the present invention includes a wavelength scanning light source that periodically scans the oscillation wavelength of light, and irradiates the reference light and the object with light from the wavelength scanning light source. An interference optical meter that branches into light and generates interference light between reflected light from an object and reference light, a light receiving element that receives the interference light obtained from the interference optical meter and obtains a beat signal, and the light receiving element A signal analysis unit that performs frequency analysis on the interference signal obtained from the signal and forms a tomographic image of the object, and the signal analysis unit holds the interference signal obtained from the light receiving element as an analysis target signal A storage unit, reading out the analysis target signal stored in the storage unit, a sine wave model signal represented by the analysis target signal, a phase using a frequency f ′ and an initial phase φ ′, and an amplitude A ′; The sum of squared differences is the minimum value The calculation means for calculating the frequency f ′, the amplitude A ′, and the initial phase φ ′, and outputting a cross-sectional image based on the obtained frequency f ′, the amplitude A ′, and the initial phase φ ′. And a display unit for displaying a cross-sectional image obtained from the calculation means.

  In order to solve this problem, an optical tomographic image display system according to the present invention includes a light source that oscillates light having a uniform wavelength within a predetermined range, light from the light source as reference light and irradiation light on an object. An interferometer that branches and generates interference light between reflected light from an object and reference light, wavelength spectroscopic means that splits the interference light obtained from the interferometer based on the wavelength, and spectral spectroscopy from the wavelength spectroscopic means A one-dimensional light receiving element that receives interference light in a specified range and converts it into an electrical signal, and a signal analysis unit that performs frequency analysis on the interference signal obtained from the one-dimensional light receiving element and forms a tomographic image of the object, The signal analysis unit reads out the analysis target signal stored in the storage unit, a storage unit that holds an interference signal obtained from the light receiving element as an analysis target signal, and the analysis target signal, Frequency f ′ and initial phase The frequency f ′, the amplitude A ′, and the initial phase φ ′ are calculated such that the sum of squares of the difference between the phase using “and the sine wave model signal represented by the amplitude A ′ is minimized. A calculating means for outputting a cross-sectional image based on the obtained frequency f ′, the amplitude A ′, and the initial phase φ ′, and a display unit for displaying the cross-sectional image obtained from the calculating means. is there.

  Here, the calculating means obtains appropriate initial values for each of the frequency f ′, the amplitude A ′, and the initial phase φ ′, and converges the obtained initial value to an optimal solution of a nonlinear equation to thereby obtain the frequency f ', The amplitude A', and the initial phase φ 'may be obtained.

  Here, the arithmetic means converges the frequency f ′ and the initial phase φ ′ constituting the phase of the sine wave model signal by applying a steepest descent method to obtain the frequency f ′ and the initial phase φ ′. The amplitude A ′ as a coefficient of the sine wave model signal may be converged by applying a steepest descent method to obtain the amplitude A ′.

  Here, the computing means applies the steepest descent method to converge the frequency f ′ and the initial phase φ ′, and further applies the Newton method to obtain the frequency f ′ and the initial phase φ ′. You may make it converge.

  Here, it further includes a k-trigger generation unit that generates a trigger signal at equal frequency intervals of the light of the wavelength scanning light source within one scanning period of the wavelength scanning light source, and the storage unit of the signal analysis unit includes The interference signal may be held at the timing of the k trigger signal generated by the k trigger generation unit.

  Here, the calculation means of the signal analysis unit takes in the output from the light receiving element at equal time intervals with a data number when a reflecting object is arranged at the measurement position of the object, and becomes the peak of the beat signal. Calculate the data number, calculate an approximate curve indicating the data number relative to the peak number, divide the peak number change into an arbitrary number, calculate the data number corresponding to the divided peak number using the approximate curve, and import the data Calculate the signal level of the timing at each element of the data acquisition number sequence from the output of the equal time interval from the light receiving element when the measurement object is arranged at the measurement position, and obtain the data of the equal frequency interval May be held in the storage means.

  According to such an optical tomographic image display system according to the present invention, formulation is performed for the purpose of frequency analysis assuming an aperiodic signal when the interference light signal is subjected to frequency analysis, and parameters of the Fourier transform equation of the aperiodic signal are set. The frequency resolution does not depend on the analysis window length by replacing the problem to be found with the problem of finding the optimal solution of the nonlinear equation. Therefore, the frequency analysis can be performed with a surprisingly high accuracy of 100,000 to 10 billion times or more compared with the accuracy in the conventional frequency analysis method using Fourier transform, and an effect that a tomographic image can be displayed with a high resolution can be obtained. It is done.

FIG. 1 is a block diagram showing an overall configuration of an optical tomographic image display system according to a first embodiment of the present invention. FIG. 2 is a block diagram showing the configuration of the k trigger generation unit of the optical tomographic image display system according to the embodiment of the present invention. FIG. 3 is a block diagram showing the configuration of the signal analysis unit of the optical tomographic image display system according to the embodiment of the present invention. FIG. 4 is a graph showing an example of the relationship between the scanning angle and the oscillation frequency. FIG. 5 is a diagram for explaining the difference between the present frequency analysis method and the DFT. FIG. 6 is a diagram for explaining the difference between the present frequency analysis method and the DFT, and is a diagram showing a specific example when each method is applied to a two-dimensional analysis target signal. FIG. 7 is a diagram for explaining the difference between the present frequency analysis method and DFT and GHA, and is a diagram showing a result of obtaining an error of each method. FIG. 8 is a diagram for explaining the difference between the present frequency analysis method and DFT, and is a diagram showing a specific example of spectrum analysis accuracy obtained by applying each method to a two-dimensional analysis target signal. FIG. 9 is a block diagram showing an overall configuration of an optical tomographic image display system according to the second embodiment of the present invention.

DESCRIPTION OF SYMBOLS 10 Wavelength scanning light source 11, 14, 18 Optical fiber 15, 19, 22 Lens 16 Reference mirror 20 Scanning mirror 23 Photodiode 24 Amplifier 25 Signal analysis part 26 Scan trigger generation part 27 k trigger generation part 31 Clock generation circuit 32 Trigger generation Circuit 33 Memory 34 RW control unit 40 Light source 41 Diffraction grating 42 One-dimensional CCD
43 Amplifier 50 Input Interface 51 CPU
52 ROM
53 RAM
54 Storage Unit 55 Input Operation Control Unit 56 Display Unit

(First embodiment)
[Configuration of optical tomographic image display system]
FIG. 1 is a block diagram showing an overall configuration of an optical tomographic image display system according to a first embodiment of the present invention. This embodiment is an optical tomographic image display system based on SS-OCT, and uses a wavelength scanning light source as a light source. The wavelength scanning light source 10 uses a wavelength variable laser that oscillates an optical signal in a certain frequency range. The output of this laser is given to the branching section 12 through the optical fiber 11. An optical amplifier 13 is provided at the other end of the optical fiber 11. The optical amplifier 13 amplifies the laser beam of the wavelength scanning light source 10 as it is, and its output is given to the optical fiber 14. A collimator lens 15 and a reference mirror 16 are provided at the other end of the optical fiber 14. Further, a coupling portion 17 is provided in the middle portion of the optical fiber 14 so that another optical fiber 18 is brought close to and interferes therewith. At one end of the optical fiber 18, a collimator lens 19 that converts an optical signal obtained from the wavelength scanning light source 10 through the coupling unit 17 into parallel light, and a scanning mirror 20 that scans the light are provided. The scanning mirror 20 changes the reflection angle of parallel light by rotating within a certain range about an axis perpendicular to the paper surface. The converging lens 21 is disposed at a position where the reflected light is received, condenses the light to the measurement site, and scans (scans) in the horizontal direction. Here, the optical distance L1 from the coupling portion 17 to the reference mirror 16 is set equal to the optical distance L2 from the coupling portion 17 to the surface of the measurement site. A photodiode 23 is connected to the other end of the optical fiber 18 via a lens 22. The photodiode 23 is a light receiving element that receives the reflected light from the reference mirror 16 and the interference light of the light reflected by the measurement site to obtain the beat signal as an electrical signal. Here, the optical fibers 14 and 18, the coupling portion 17, the collimating lens 15, the reference mirror 16, the collimating lens 19, the scanning mirror 20, and the focusing lens 21 constitute an interference optical meter.

  The output of the photodiode 23 is input to the signal analysis unit 25 via the amplifier 24. The signal analysis unit 25 obtains a tomographic image signal by converting a light reception signal obtained from the interferometer into a frequency domain signal, as will be described later.

  A part of the output of the wavelength scanning light source 10 is branched by the branching section 12 and supplied to the scan trigger generating section 26. The scan trigger generator 26 generates a scan trigger signal indicating the start of one scan of light from the wavelength scanning light source 10. The k-trigger generator 27 generates a large number of k-trigger signals at equal frequency intervals within one scanning range based on the scan trigger signal. This k trigger signal is input to the signal analysis unit 25.

Next, FIG. 2 is a diagram illustrating a configuration of the k trigger generation unit 27. The k trigger generation unit 27 includes a clock generation circuit 31, a trigger generation circuit 32, and a memory 33 as disclosed in Patent Document 2. The clock generation circuit 31 generates a clock signal at a constant timing. The memory 33 can be arbitrarily rewritten by the RW control unit 34 that controls reading and writing. This memory 33 uses the oscillation frequency f (f1 ≦ f ≦ f2) of the wavelength scanning light source 10 as a function of time, and f = f (t)
If the timings at which the frequency change range δf is equally spaced are t ₁ , t ₂ ... T _m ... T _n (m = 1 to n), the oscillation frequency f shown by the following equation: (T _m ) = f1 + (m−1) δf
T _m = f ⁻¹ {f1 + (m−1) δf}
As a table. The trigger generation circuit 32 reads out data from the memory 33 each time a trigger signal is input, thereby generating a k trigger signal at equal frequency intervals.

[Configuration of signal analyzer]
The signal analysis unit 25 realizes a new frequency analysis method in which the frequency resolution does not depend on the analysis window length by solving the nonlinear equation and estimating the Fourier coefficient. For example, as shown in FIG. 3, the signal analysis unit 25 is an input interface (IF) 50, a CPU (Central Processing Unit) 51 that centrally controls each unit, and a read-only storage that stores various types of information including various programs. A ROM (Read Only Memory) 52, a RAM (Random Access Memory) 53 that functions as a work area, a storage unit 54 that stores various information in a readable and / or writable manner, and a predetermined operation device (not shown) as a user interface An input operation control unit 55 that performs processing and control of input operations via the computer, and a display unit 56 that displays various types of information.

  The input interface unit 50 has a function of allowing the CPU 51 to input an analysis target signal so as to be read out. The input interface has a function of converting the output of the amplifier 24 into a digital signal by performing A / D conversion when the k trigger signal is input. At this time, the input interface may include an anti-aliasing filter as necessary.

  The CPU 51 executes various programs including various application programs stored in the storage unit 54 and the like, and comprehensively controls each unit.

  The ROM 52 stores various information including various programs. The RAM 53 functions as a work area when the CPU 51 executes various programs. The CPU 51 temporarily stores various types of information in the RAM 53 and reads various types of information stored in the ROM 52 and the RAM 53.

  In addition to the application program such as the signal analysis program according to the present invention, the storage unit 54 stores various types of information including data of an analysis target signal that is a target of frequency analysis. As this memory | storage part 54, a hard disk, a non-volatile memory, etc. can be used, for example. The storage unit 54 also includes a drive device that reads and / or writes various types of information on a storage medium such as a flexible disk or a memory card that can be attached to and detached from the main body. Various information stored in the storage unit 54 is read under the control of the CPU 51.

  For example, the input operation control unit 55 receives an input operation through a predetermined operation device serving as a user interface such as a keyboard, a mouse, a keypad, an infrared remote controller, a stick key, or a push button, and indicates a control signal indicating the operation content Is supplied to the CPU 51.

  The display unit 56 is various display devices such as a liquid crystal display, for example, and displays various types of information under the control of the CPU 51. For example, when the signal analysis program is activated by the CPU 51, the display unit 56 displays the screen and displays the input analysis target signal, the frequency analysis result, and the like.

[Principle of optical coherent tomography]
Next, the principle of optical coherent tomography using a wavelength scanning light source will be described. The backscattered light reflected from the inside of the object or the subepidermal layer of the living body by irradiating the target object with coherent light whose optical frequency continuously and periodically changes from the light source, and using an interference optical meter such as Michelson or Mach-Zehnder Interfere with the reference beam. By measuring the intensity distribution of the interference light and measuring the change in the intensity distribution corresponding to the change in the optical frequency, a tomographic image along the depth direction can be constructed. Further, by scanning a spatial beam in one dimension and two dimensions on the object, a two-dimensional and three-dimensional tomographic image can be constructed, respectively.

In the interferometer, when the optical path of the two arms from the coupling unit 17, that is, the optical path L1 to the reference mirror 16 and the optical path L2 to the reflecting surface in the object are equal, the beat frequency of the interference light is zero. Next, when the reflected light is reflected from a certain depth z inside the object, if the optical frequency changes with time, the reflected light from the object and the reflected light from the reference mirror 16 are equivalent to the difference in the optical path. A difference occurs in frequency, and a beat occurs in the interference light. Here, for example, it is assumed that the optical frequency of the light source is scanned linearly in terms of time. It is assumed that the surface of the object is at a position where the lengths of the arms of the interferometer are equal, and the reflecting surface of the object is only at a position at a depth z from the surface. The temporal changes in the frequency of the reference light and the frequency of the light reflected from the object (object light) at the coupling unit 17 are as shown by straight lines A and B in FIG. Here, the optical frequency is scanned at a scanning rate α [Hz / s] over a frequency width Δf = αT [Hz] within a time T [s]. The delay time τ of the object light with respect to the reference light is expressed as follows:
τ = 2 nz / c
It becomes. Therefore, the interference light received by the photodiode 23 has a beat frequency fb = ατ = (Δf / T) (2 nz / c).
Will fluctuate.

  Actually, since the reflected light is continuously generated from different positions along the depth inside the object, the reflected light has different beat frequency components corresponding to each depth. Therefore, the intensity of reflected light from a specific depth corresponding to the beat frequency can be detected by frequency analysis of the intensity change of the interference light. A tomographic image can be constructed by taking the spatial distribution of the reflection intensity.

I _dct = (ηq / hν) {Pr + Po∫r (z) dz + 2 (PrPo) ^1/2
R (z) cos (2k (t) z + φ) dz}
The first and second terms of the interference light signal I _dct are the reference mirror and the direct current component of the reflected light from the object, respectively, the third term is the interference signal light component, and in equation (2), Pr is the reference light intensity, Po represents the probe light intensity r (z) and the reflectance distribution in the depth direction. By analyzing the frequency of the interference light signal of I _dct , the relationship of scattered light intensity corresponding to an arbitrary depth in the object can be obtained. The signal analysis unit 25 of the present invention uses the interference light signal I _dct represented by this equation as the analysis target signal X (n) and performs frequency analysis by non-harmonic analysis.

[Operation of optical tomographic image display system]
Next, the operation of the present embodiment will be described. The wavelength scanning light source 10 is driven. As a result, the signal light is irradiated to the reference mirror and the object through the optical fibers 14 and 18 as described above, and the reflected light is obtained through the coupling portion 17. A signal having the beat frequency is obtained in the photodiode 23. A light reception signal obtained by amplifying the signal is input to the signal analysis unit 25. Further, as described above, k-trigger signals at equal frequency intervals are obtained from the k-trigger generating unit 27, A / D conversion is performed in accordance with the k-trigger signals, and the received light signal is frequency-analyzed by the signal analyzing unit 25. A one-dimensional tomographic image is obtained in the vertical direction. Then, by rotating the scanning mirror 20, the incident position of the light is changed, whereby a two-dimensional cross-sectional image can be obtained. Further, a three-dimensional cross-sectional image can be obtained by moving the interferometer itself or the measurement object in a direction perpendicular to the light scanning direction by the scanning mirror 20.

  Next, the processing of the signal analysis unit 25 will be described in more detail. Under the control of the CPU 51, the signal analysis program is executed to analyze the frequency of the input signal. The analysis target signal X (n) that is the target of frequency analysis is input via the signal input interface 50 and is stored in the storage unit 54 so as to be readable by the CPU 51. Under the control of the CPU 51, the signal analysis unit 25 performs frequency analysis of the analysis target signal input in this manner, and displays and outputs the analysis result and the like on the display unit 56.

[Frequency analysis algorithm]
Hereinafter, the frequency analysis algorithm in the signal analysis unit 25 will be described in detail. The frequency analysis method newly proposed by the signal analysis unit 25 of the present invention (hereinafter referred to as the present frequency analysis method) is “the relationship between finely capturing changes in frequency and increasing frequency resolution are mutually contradictory. In order to essentially solve the problem of the conventional frequency analysis method of “There is”, we focused on the problem of finding the solution of the nonlinear equation. That is, in this frequency analysis method, the problem of obtaining the frequency parameter of the Fourier transform equation of the aperiodic signal shown in the following equation (3) is replaced with the problem of obtaining the optimal solution of the nonlinear equation.

Specifically, in this frequency analysis method, as shown in the following equation (4), as an optimal solution of a nonlinear equation represented by the sum of squares of the difference between the analysis target signal x (n) and the sine wave model signal: Then, the frequency f ′, the amplitude A ′, and the initial phase φ ′ are obtained so that the right side of the nonlinear equation becomes the minimum value. In the following equation (4), L is a frame length (analysis window length), and f _s is a sampling frequency [Hz]. Thus, incorporating the frequency f ′ as a parameter in the nonlinear equation is novel with no examples yet. In other words, in this frequency analysis method, the objective is to accurately determine not only the amplitude A ′ and the initial phase φ ′ but also the frequency f ′, and the solution of the nonlinear equation is used for the above equation (3). Is. In this frequency analysis method, the effect of the analysis window and aliasing are eliminated by reducing the problem of finding the optimal solution of the nonlinear equation by the least square method, and the analysis window length is less than one cycle. In addition, it is not necessary to be an integral multiple of the period, and furthermore, it is possible to realize flexible frequency analysis processing such as unequal intervals.

The above equation (4) assumes that the analysis target signal x (n) is a one-dimensional signal such as a light reception signal or a time-series signal, but the frequency analysis method itself is a two-dimensional image. The present invention can also be applied to two-dimensional signals such as data, three-dimensional signals such as moving image data, four-dimensional signals such as three-dimensional moving image data such as holograms, and signals of higher dimensions. That is, this frequency analysis method uses s (x _n ) for a one-dimensional analysis target signal, s (x _m , y _n ) for a two-dimensional analysis target signal, and s (x _l , y for a three-dimensional analysis target signal. _m , z _n ) When a four-dimensional analysis target signal is generalized as s (x _k , y _l , z _m , w _n ), the analysis target signal is one-dimensional, two-dimensional, three-dimensional, or four-dimensional For each of these, the optimal solution of the nonlinear equation shown in the following equations (5) to (8) is obtained.

In other words, this frequency analysis method generalizes an arbitrary n-dimensional (n is an integer of 1 or more) analysis target signal as s (x1 _n1 , x2 _n2 , x3 _n3 ,..., Xn _nn ). The optimum solution of the nonlinear equation shown in the following equation (9) is obtained.

  In the following, for the sake of convenience of explanation, it is assumed that the analysis target signal is one-dimensional and an optimal solution of the nonlinear equation shown in the above equation (4) is obtained.

  In order to actually obtain the optimum solution of the nonlinear equation shown in the above equation (4), the following method can be used.

  In this frequency analysis method, appropriate initial values are obtained for each of the amplitude A ′, the frequency f ′, and the initial phase φ ′, and converged to an optimal solution from these initial values using a solution of a nonlinear equation. In this nonlinear problem, the above equation (4) is a minimization problem with a cost function. Appropriate initial values can be obtained by performing an arbitrary frequency transform such as a discrete Fourier transform (hereinafter referred to as DFT) or wavelet transform, or by providing an approximate register by performing filtering. Any method can be applied.

First, in this frequency analysis method, a so-called steepest descent method is applied to the frequency parameters f ′ and φ ′ constituting the phase of the sine wave model signal in the above equation (4), and the frequency parameters f _m ′ and φ _m ′ are applied. Is obtained by the following equations (10) and (11).

In addition, in the above formula (10) and the above formula (11), it is abbreviated as the following formula (12). Further, mu _m, a weighting factor based on the so-called reduction method, to a cost function determined by the recursion formula monotonically decreasing sequence takes a value of timely 0-1.

If the frequency parameters f _m ′ and φ _m ′ can be obtained, the frequency parameter A ′ as a coefficient of the sine wave model signal in the above equation (4) can be uniquely obtained. The frequency parameter A _m ′ is converged by equation (13).

  In this frequency analysis method, it is possible to converge the amplitude A ′, the frequency f ′, and the initial phase φ ′ with high accuracy by repeatedly performing these series of calculations. In particular, in this frequency analysis method, the calculation is performed by separately obtaining the frequency parameters f ′ and φ ′ constituting the phase of the sine wave model signal in the above equation (4) and the frequency parameter A ′ as a coefficient. It can be performed simply.

  However, although the steepest descent method converges from a relatively wide range, the accuracy is low in one iteration, and it takes time to converge.

Therefore, in this frequency analysis method, it is desirable to converge the frequency parameters f _m ′ and φ _m ′ to some extent by applying the steepest descent method, and then to converge with high accuracy by applying the so-called Newton method. . Specifically, in this frequency analysis method, the frequency parameters f _m ′ and φ _m ′ are obtained by the recurrence formulas shown in the following equations (14) and (15) as the Newton method.

However, in the above formula (14) and the above formula (15), J is the following formula (16) and is abbreviated as the following formula (17). Also, [nu _m is also a weighting coefficient based on the reduction method in the same manner as mu _m, taking the value of timely 0-1.

In the present frequency analysis technique, the above equation (14) and the above equation (15) frequency parameter f _m by ', phi _m' sought after, like the steepest descent method, frequency parameter by the above equation (13) A _m 'Is converged and this series of calculations is repeated further.

  As described above, in this frequency analysis method, the frequency parameters A ′, f ′, and φ ′ are estimated at high speed and with high accuracy by using a hybrid method combining the steepest descent method and the Newton method. Can do.

  Further, in this frequency analysis method, even if the analysis target signal x (n) is a composite sine wave, the spectral parameter can be approximately derived by performing successive subtraction processing. Here, it is assumed that the analysis target signal x (n) is the sum of a plurality of sine waves and is represented by the following equation (18).

According to the Parseval theorem, when the frequency f _{k of the} analysis target signal x (n) and the frequency parameter f ′ of the sine wave model signal do not coincide at all, that is, when the following equation (19) is satisfied, The nonlinear equation shown in the equation (4) becomes the following equation (20). The frequency parameter f ', phi' pairs are if it matches one of the set of frequency f _k and the initial phase phi _k is nonlinear equation shown in the above equation (4) becomes the following equation (21) . Further, when the amplitude A _j matches the frequency parameter A ′, the frequency component related to the estimated spectrum can be completely eliminated from the analysis target signal. Therefore, the problem of obtaining the optimum solution is independent of the frequency, and can be applied to signals represented by a plurality of sine waves if individually estimated from the analysis target signal.

  That is, in this frequency analysis method, even if the analysis target signal x (n) is a composite sine wave, it is possible to extract a plurality of sine waves by performing the same process on the residual signal successively. .

  However, in the case of a plurality of spectra, an infinite length is assumed, as can be seen from the above equation (3). Therefore, when the frequencies of the plurality of spectra are close to each other, the period of the combined spectrum is the analysis window length. In some cases, an error occurs because the above equation (17) is not satisfied.

  In the conventional OCT, a large number of spectra (number of sine waves) is required to express a received light signal by a composite sine wave. However, in this frequency analysis method, even such a signal is a little. The number of spectra can be expressed without error. In other words, the ability to represent a signal with a smaller number of spectrums is useful for information compression applications, and besides that, by using an approach that expresses a wave number with respect to a physical phenomenon, It shows that the essential characteristics of the signal can also be seen.

[Effectiveness of this frequency analysis method]
Hereinafter, the effectiveness of this frequency analysis method will be specifically described.

  Conventionally, in order to analyze a signal measured by a sensor using a computer, generally, as shown in FIG. 5, for example, a part of the signal is cut out by a typical harmonic frequency analysis method such as DFT. I was analyzing.

  However, when the analysis target signal is cut out (windowed) and the harmonic analysis is performed, the analysis target signal is assumed to be a signal in which a part of the cut out signal is repeated in a complete cycle. Of course, of course, the frequency characteristic is not completely identical to the original spectral characteristic. In addition, in order to avoid the influence of the signal clipping, attempts have been made to reduce the influence by a window function. Currently, no solution has been reached.

  On the other hand, this frequency analysis method is formulated for the purpose of frequency analysis assuming non-periodic signals. Therefore, the frequency and its parameters can be accurately determined without being restricted by the analysis window length and frequency resolution. Can be estimated.

  In addition, this frequency analysis method is also an innovative method that can significantly improve accuracy since frequency estimation is changed from a conventional discrete search to a dynamic and continuous search.

  Further, regarding multi-dimensionalization, the conventional frequency analysis method is affected by the window function as in the case where the analysis target signal is one-dimensional. Specifically, for example, as shown in FIG. 6, even if a broken line portion in the left diagram of FIG. 6 is cut out from the two-dimensional analysis target signal (original image data) and analyzed by performing DFT, the cut out section Since this is equivalent to analyzing an image with a complete period repeated repeatedly, as shown in the upper right figure, the restored image data is affected by the window function, and the essential characteristics are It is difficult to find.

  On the other hand, in the present frequency analysis method to which the above equation (6) is applied, the influence of the window function is reduced as shown in the lower right diagram of FIG. Therefore, an essential frequency characteristic can be found, and an image around the cut-out section can be completely reproduced.

  As described above, this frequency analysis method can obtain the frequency f ′, the amplitude A ′, and the initial phase φ ′ of the sine wave model signal at high speed and with high accuracy by obtaining the optimal solution of the nonlinear equation. . In order to verify the specific accuracy, the inventor of the present application verified accuracy by comparing DFT and GHA (Generalized Harmonic Analysis), which is said to have the highest analysis accuracy among the developed types of DFT. .

  Note that DFT and GHA apparently have a plurality of window lengths in one analysis window length, so the frequency resolution depends on the analysis window length, but the resolution frequency is finite, and the signal to be analyzed If the analysis signal is different from the frequency that can be analyzed accurately, the analysis signal cannot be analyzed when the frequency becomes a frequency other than the decomposition frequency. A frequency (sideband component) appears, and a plurality of frequencies appear.

  Whether or not such a phenomenon occurs also in the present frequency analysis method, that is, in order to verify the frequency resolution of the present frequency analysis method, the analysis window length is one second (1024 samples) and is very short. A single sine wave was analyzed, one sine wave was extracted by each method, and the square error from the original signal was examined. The result is shown in FIG.

  As shown in FIG. 7, in the DFT, the analysis accuracy deteriorated at frequencies other than an integral multiple of the fundamental frequency. In addition, in GHA, an accuracy improvement of about 2 to 5 digits was observed compared with DFT at a frequency of 1 Hz or higher. On the other hand, in this frequency analysis method, an accuracy improvement of 10 digits or more compared to DFT and 5 digits or more compared to GHA was observed at a frequency of 1 Hz or more. That is, this frequency analysis method showed an improvement in accuracy of 100,000 to 10 billion times or more compared with the existing frequency analysis method.

  In particular, the ability to accurately estimate frequencies below 1 Hz indicates that analysis is possible even with long periodic signals that exceed the analysis window length, and the spectral structure can be estimated more accurately. It is shown that.

  As described above, this frequency analysis method can perform analysis with surprisingly high accuracy even compared to GHA, which is said to have the highest analysis accuracy. Looking at various research cases in Japan and overseas, there is no method that can analyze signals with such accuracy, and this frequency analysis method is expected to be applied to various fields that require accurate analysis in the future. It can be said that this is a possible technique.

[Image coding]
In this frequency analysis method, since the influence of the window is small, no sideband component appears in the spectrum. In other words, as described above, this frequency analysis method can efficiently express even a complicated analysis target signal with a small number of spectra without error.

  FIG. 8 shows specific examples in which a two-dimensional signal is analyzed by the DFT and the frequency analysis method. As shown in the left diagram of FIG. 8, when a signal originally expressed by one spectrum is converted by DFT, in general, the spectrum obtained by conversion is also caused by the influence of the analysis window, As shown in the upper right diagram in FIG. 8, a plurality of sideband components appear together. The same applies to discrete cosine transform (DCT), which is widely used in image compression coding. On the other hand, this frequency analysis method can accurately estimate the spectrum of the original signal as shown in the lower right diagram of FIG. If it can be analyzed accurately, the number of spectra representing image data may be significantly reduced, and a dramatic information compression effect can be expected without degrading image quality.

  In this embodiment, a high resolution image can be obtained without widening the scanning range of the wavelength scanning light source. Therefore, a tomographic image having a necessary resolution can be obtained by using an inexpensive wavelength scanning light source that could not be used conventionally. If a light source capable of scanning a wide range of wavelengths is used, a more accurate cross-sectional image can be obtained.

  In this embodiment, the k-trigger generation unit generates a large number of k-trigger signals at the same frequency interval during one wavelength scanning, but the scan trigger signal only discloses one wavelength scan. It is good. In this case, as shown in Japanese Patent Application Laid-Open No. 2008-261778, when a reflector is placed at the measurement position of the object, the output from the light receiving element is fetched at equal time intervals with data numbers, and the peak of the beat signal is detected. The data number corresponding to the divided peak number is calculated by the approximate curve by dividing the peak number change into an arbitrary number. Then, the data acquisition number sequence may be used, and the timing at each element of the data number sequence may be given to the signal analysis unit as a trigger signal from the output from the equal time interval from the light receiving element when the measurement object is arranged.

(Second Embodiment)
FIG. 9 is a block diagram showing an overall configuration of an optical tomographic image display system according to the second embodiment of the present invention. The present embodiment is an optical tomographic image display system based on SD-OCT, and uses a light source 40 that emits uniform light in a predetermined wavelength range as a light source. The light from the light source 40 is guided to the optical interferometer via the optical amplifier 13 as in the first embodiment. In this embodiment, the light obtained by the lens 22 is incident on the diffraction grating 41. The diffraction grating 41 is a wavelength spectroscopic unit that disperses light according to the wavelength of incident light, and the dispersed light is input to the one-dimensional CCD 42. The one-dimensional CCD 42 converts the optical signal at each position into a one-dimensional light receiving signal at a predetermined cycle, and the output is transmitted to the signal analysis unit 25 via the amplifier 43. In this case, the trigger signal is transmitted to the input interface periodically at the timing of output from each one-dimensional pixel of the CCD 42. The subsequent configuration is the same as that of the first embodiment. A tomographic image can be obtained in the same manner even if the frequency is analyzed based on the light reception signal obtained by the one-dimensional CCD in this way.

  Although the signal analysis apparatus in the above-described embodiment has been described as performing frequency analysis by software, the present invention performs product-sum operations such as a DSP (Digital Signal Processor) that implements the algorithm of this frequency analysis method. If possible, it can also be realized by hardware.

  Thus, it goes without saying that the present invention can be modified as appropriate without departing from the spirit of the present invention.

Claims (7)

A wavelength scanning light source that periodically scans the oscillation wavelength of light;
An interference optical meter for branching light from the wavelength scanning light source into reference light and irradiation light to the object, and generating interference light between the reflected light from the object and the reference light;
A light receiving element that receives interference light obtained from the interference optical meter and obtains a beat signal;
A frequency analysis is performed on the interference signal obtained from the light receiving element, and a signal analysis unit that forms a tomographic image of the object, and
The signal analysis unit
A storage unit for holding an interference signal obtained from the light receiving element as an analysis target signal;
The analysis target signal stored in the storage unit is read out, and the square of the difference between the analysis target signal and the sine wave model signal represented by the phase using the frequency f ′ and the initial phase φ ′ and the amplitude A ′ The frequency f ′, the amplitude A ′, and the initial phase φ ′ are calculated such that the sum is a minimum value, and the cross-sectional image is based on the obtained frequency f ′, the amplitude A ′, and the initial phase φ ′. Calculating means for outputting
An optical tomographic image display system comprising: a display unit configured to display a cross-sectional image obtained by the calculation unit. A light source that oscillates light of a uniform wavelength within a predetermined range;
An interferometer that branches the light from the light source into reference light and irradiation light to the object, and generates interference light between the reflected light from the object and the reference light;
Wavelength spectroscopy means for branching interference light obtained from the interference optical meter based on the wavelength;
A one-dimensional light receiving element that receives interference light in a range separated by the wavelength spectroscopic means and converts it into an electrical signal;
A frequency analysis is performed on the interference signal obtained from the one-dimensional light receiving element, and a signal analysis unit that forms a tomographic image of the object is provided.
The signal analysis unit
A storage unit for holding an interference signal obtained from the light receiving element as an analysis target signal;
The analysis target signal stored in the storage unit is read out, and the square of the difference between the analysis target signal and the sine wave model signal represented by the phase using the frequency f ′ and the initial phase φ ′ and the amplitude A ′ The frequency f ′, the amplitude A ′, and the initial phase φ ′ are calculated such that the sum is a minimum value, and the cross-sectional image is based on the obtained frequency f ′, the amplitude A ′, and the initial phase φ ′. Calculating means for outputting
An optical tomographic image display system comprising: a display unit configured to display a cross-sectional image obtained by the calculation unit.   The calculation means obtains appropriate initial values for each of the frequency f ′, the amplitude A ′, and the initial phase φ ′, and converges the obtained initial value to an optimal solution of a nonlinear equation to obtain the frequency f ′, The optical tomographic image display system according to claim 1, wherein the amplitude A ′ and the initial phase φ ′ are obtained.   The arithmetic means converges the frequency f ′ and the initial phase φ ′ constituting the phase of the sine wave model signal by applying a steepest descent method to obtain the frequency f ′ and the initial phase φ ′, 4. The optical tomographic image display system according to claim 3, wherein the amplitude A ′ as a coefficient of a sine wave model signal is converged by applying a steepest descent method to obtain the amplitude A ′.   The computing means applies the steepest descent method to converge the frequency f ′ and the initial phase φ ′, and further applies the Newton method to converge the frequency f ′ and the initial phase φ ′. The optical tomographic image display system according to claim 4. A k-trigger generator for generating trigger signals at equal frequency intervals of the light of the wavelength scanning light source within one scanning period of the wavelength scanning light source;
The optical tomographic image display system according to claim 1, wherein the storage unit of the signal analysis unit holds the interference signal at the timing of the k trigger signal generated by the k trigger generation unit. The calculation means of the signal analysis unit is:
When a reflector is placed at the measurement position of the object, the output from the light receiving element is captured at equal time intervals with a data number, and the data number that becomes the peak of the beat signal is calculated. Approximate curve is calculated, the change in peak number is divided into an arbitrary number, the data number corresponding to the divided peak number is calculated by the approximate curve to obtain a data acquisition number sequence, and the measurement object is arranged at the measurement position A signal level of timing at each element of the data acquisition number sequence is calculated from an output at equal time intervals from the light receiving element, and the obtained data at equal frequency intervals is held in the storage means. Item 4. The optical tomographic image display system according to Item 1.

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